Question: Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. $\begin{array}{r} x-1 \\ x-2|\overline{x^2-3x+9} \\ \mathllap{-(}\underline{x^2-2x\phantom{+9}\rlap )} \\ -x+9 \\ \mathllap{-(}\underline{-x+2\rlap )} \\ 7 \end{array}$ We get that the quotient is $x-1$ and the remainder is $7$, and therefore: $\dfrac{x^2-3x+9}{x-2}=x-1+\dfrac{7}{x-2}$ [I want to see a different way of performing the division.]